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The nLab
By far the best site to learn about category and higher category theory.
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OreModules
OreModules is a Maple implementation of algorithms which compute parametrizations, extension modules (ext), resolutions and other algebraic objects for linear systems of differential equations, time-delay systems, etc. The package OreModules, based on an original program by F. Chyzak and A. Quadrat, is maintained and further developed by A. Quadrat and D. Robertz.
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OreMorphisms
The package OreMorphisms is based on OreModules devoted to the symbolic study of multidimensional systems. It was developed by T. Cluzeau and A. Quadrat.
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homalg in Maple (discontinued)
A meta-package for homological algebra. This is the (discontinued) Maple package homalg - the early stages of the homalg project.
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The Kenzo program
A program for constructive algebraic topology
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CHA - Computational Homological Algebra
Computational Homological Algebra
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GAP
GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra
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Singular
SINGULAR is a Computer Algebra System for polynomial computations with special emphasis on the needs of commutative algebra, algebraic geometry, and singularity theory.
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Macaulay2
A new software system devoted to supporting research in algebraic geometry and commutative algebra.
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Sage
Sage: Open Source Mathematics Software
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MAGMA
MAGMA Computational Algebra System
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Maplesoft
The company developing Maple.
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